Question

Test the hypothesis using the​ P-value approach. Be sure to verify the requirements of the test.

H0​: p=0.2 versus H1​: p>0.2

n=200​; x=55, α=0.1

Is np0(1−p)0≥​10?

Yes

No

Use technology to find the​ P-value.

​P-value=__?__

​(Round to three decimal places as​ needed.)

▼

Do not reject

Reject

the null​ hypothesis, because the​ P-value is

▼

greater

less

than α.

Answer 1

Solution :

This is the rigth tailed test .

= x / n = 55 / 200 = 0.275

P₀ = 0.2

1 - P₀ = 0.2

n P₀ (1 - P₀ ) = 200 * 0.2 * 0.8 = 32

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.275 - 0.2 / [(0.2 * 0.8) / 200]

= 2.65

P(z > 2.65) = 1 - P(z < 2.65) = 0.004

P-value = 0.004

= 0.1

P-value <

Reject the null hypothesis .